To Expand an Expression in a Taylor or Laurent Series
• Place the cursor at the end of a function, insert the symbolic evaluation operator, and type the keyword series in the placeholder.
The resulting series contains a large number of terms with non-zero coefficients of odd and even powers of x, but PTC Mathcad returns, by default, the first six terms.
• To return a different number of terms, type a comma after the keyword, followed by a positive integer k. If the first non-zero term of the series corresponds to xn, then PTC Mathcad returns the terms from xn to xn+k-1.
The following evaluation calls for returning 8 terms of the series for the sin function. Since the first non-zero term of the series corresponds to x1, PTC Mathcad returns the terms between x1 and x8.
Terms that have coefficients of 0 are not displayed.
• If the function contains more than one variable, type a comma after series, and then type a comma-separated list of variables around which you want to expand. By default, PTC Mathcad expands the function about point 0. To expand around a point other than 0, specify a value for the variable after the keyword series, using the Boolean equal operator.
A Taylor series for a function may converge only in a small interval around the center. Functions like sin or exp have series with an infinite number of terms, but the returned number depends on the order you select. When you approximate a function using the polynomial returned by expanding to a series, the approximation is reasonably accurate close to the center, but it may be quite inaccurate for values far from the center.
